Tài chính doanh nghiệp - Chapter 24: Portfolio performance evaluation

Chapter 24Portfolio Performance EvaluationComplicated subjectTheoretically correct measures are difficult to constructDifferent statistics or measures are appropriate for different types of investment decisions or portfoliosMany industry and academic measures are differentThe nature of active management leads to measurement problemsIntroductionDollar-weighted returnsInternal rate of return considering the cash flow from or to investmentReturns are weighted by the amount invested in each stockTime-weighted returnsNot weighted by investment amountEqual weighting Dollar- and Time-Weighted ReturnsText Example of Multiperiod ReturnsPeriod Action 0 Purchase 1 share at $50 1 Purchase 1 share at $53 Stock pays a dividend of $2 per share 2 Stock pays a dividend of $2 per share Stock is sold at $108 per sharePeriod Cash Flow 0 -50 share purchase 1 +2 dividend -53 share purchase 2 +4 dividend + 108 shares soldInternal Rate of Return:Dollar-Weighted ReturnTime-Weighted ReturnSimple Average Return: (10% + 5.66%) / 2 = 7.83%Averaging ReturnsArithmetic Mean:Geometric Mean:Text Example Average:(.10 + .0566) / 2 = 7.81%[ (1.1) (1.0566) ]1/2 - 1 = 7.83%Text Example Average:Past Performance - generally the geometric mean is preferable to arithmeticPredicting Future Returns from historical returnsUse a weighted average of arithmetic and geometric averages of historical returns if the forecast period is less than the estimation periodUse geometric is the forecast and estimation period are equalGeometric & Arithmetic Means ComparedWhat is abnormal?Abnormal performance is measured:Benchmark portfolioMarket adjustedMarket model / index model adjustedReward to risk measures such as the Sharpe Measure:E (rp-rf) / pAbnormal PerformanceMarket timingSuperior selectionSectors or industriesIndividual companiesFactors Leading to Abnormal Performance1) Sharpe Indexrp - rfprp = Average return on the portfolio rf = Average risk free ratep= Standard deviation of portfolio returnRisk Adjusted Performance: SharpeM2 MeasureDeveloped by Modigliani and ModiglianiEquates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolioIf the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the marketM2 Measure: ExampleManaged Portfolio: return = 35% standard deviation = 42%Market Portfolio: return = 28% standard deviation = 30% T-bill return = 6%Hypothetical Portfolio:30/42 = .714 in P (1-.714) or .286 in T-bills(.714) (.35) + (.286) (.06) = 26.7%Since this return is less than the market, the managed portfolio underperformed2) Treynor Measurerp - rfßprp = Average return on the portfolio rf = Average risk free rateßp = Weighted average for portfolioRisk Adjusted Performance: TreynorRisk Adjusted Performance: Jensen3) Jensen’s Measure = rp - [ rf + ßp ( rm - rf) ]pp= Alpha for the portfoliorp = Average return on the portfolioßp = Weighted average Betarf = Average risk free raterm = Avg. return on market index port. Appraisal RatioAppraisal Ratio = ap / s(ep)Appraisal Ratio divides the alpha of the portfolio by the nonsystematic riskNonsystematic risk could, in theory, be eliminated by diversificationIt depends on investment assumptions1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market.2) If many alternatives are possible, use the Jensen or the Treynor measure The Treynor measure is more complete because it adjusts for riskWhich Measure is Appropriate?Assumptions underlying measures limit their usefulnessWhen the portfolio is being actively managed, basic stability requirements are not metPractitioners often use benchmark portfolio comparisons to measure performanceLimitationsAdjusting portfolio for up and down movements in the marketLow Market Return - low ßetaHigh Market Return - high ßetaMarket TimingExample of Market Timing***********************rp - rfrm - rfSteadily Increasing the BetaDecomposing overall performance into componentsComponents are related to specific elements of performanceExample componentsBroad AllocationIndustrySecurity ChoiceUp and Down MarketsPerformance AttributionSet up a ‘Benchmark’ or ‘Bogey’ portfolioUse indexes for each componentUse target weight structureAttributing Performance to ComponentsCalculate the return on the ‘Bogey’ and on the managed portfolioExplain the difference in return based on component weights or selectionSummarize the performance differences into appropriate categoriesAttributing Performance to ComponentsWhere B is the bogey portfolio and p is the managed portfolioFormula for AttributionContributions for Performance Contribution for asset allocation (wpi - wBi) rBi + Contribution for security selection wpi (rpi - rBi) = Total Contribution from asset class wpirpi -wBirBiTwo major problemsNeed many observations even when portfolio mean and variance are constantActive management leads to shifts in parameters making measurement more difficultTo measure wellYou need a lot of short intervalsFor each period you need to specify the makeup of the portfolioComplications to Measuring PerformanceStyle AnalysisBased on regression analysisExamines asset allocation for broad groups of stocksMore precise than comparing to the broad marketSharpe’s analysis: 97.3% of returns attributed to style